No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Reliability of parameter estimates in the first observing run of Advanced LIGO
Abstract
Accurate parameter estimation is key to maximizing the scientific impact of gravitational-wave astronomy. Parameters of a binary merger are typically estimated using Bayesian inference. It is necessary to make several assumptions when doing so, one of which is that the detectors output stationary Gaussian noise. We test the validity of these assumptions by performing percentile-percentile tests in both simulated Gaussian noise and real detector data in the first observing run of Advanced LIGO (O1). We add simulated signals to 512s of data centered on each of the three events detected in O1—GW150914, GW151012, and GW151226—and check that the recovered credible intervals match statistical expectations. We find that we are able to recover unbiased parameter estimates in the real detector data, indicating that the assumption of Gaussian noise does not adversely effect parameter estimates. However, we also find that both the parallel-tempered sampler emcee_pt and the nested sampler dynesty struggle to produced unbiased parameter estimates for GW151226-like signals, even in simulated Gaussian noise. The emcee_pt sampler does produce unbiased estimates for GW150914-like signals. This highlights the importance of performing percentile-percentile tests in different targeted areas of parameter space.
... This distribution of expected offsets can be found analytically or through simulations for the ideal case of Gaussian and stationary noise. In S. Kulkarni & C. D. Capano (2021), the authors present another method to test the assumptions of Gaussian and stationary noise in the presence of the signal: one can launch an injection-recovery campaign in the vicinity of the signal assuming the noise properties do not change in the chosen window. By studying the recovered parameters from many injections, it can be determined if the recovered credible intervals match the statistical expectations of Gaussian and stationary noise (S. ...
... In S. Kulkarni & C. D. Capano (2021), the authors present another method to test the assumptions of Gaussian and stationary noise in the presence of the signal: one can launch an injection-recovery campaign in the vicinity of the signal assuming the noise properties do not change in the chosen window. By studying the recovered parameters from many injections, it can be determined if the recovered credible intervals match the statistical expectations of Gaussian and stationary noise (S. Kulkarni & C. D. Capano 2021). ...
The sensitivity of gravitational-wave (GW) detectors is characterized by their noise curves, which determine the detector’s reach and ability to measure the parameters of astrophysical sources accurately. The detector noise is typically modeled as stationary and Gaussian for many practical purposes and is characterized by its power spectral density (PSD). However, due to environmental and instrumental factors, physical changes in the state of detectors may introduce nonstationarity into the noise. Misestimation of the noise behavior directly impacts the posterior width of the signal parameters. It becomes an issue for studies that depend on accurate localization volumes, such as (i) probing cosmological parameters (e.g., the Hubble constant) using cross-correlation methods with galaxies and (ii) doing electromagnetic follow-up using localization information from parameter estimation done from premerger data. We study the effects of dynamical noise on the parameter estimation of the GW events. We develop a new method to correct dynamical noise by estimating a locally valid pseudo-PSD normalized along a potential signal’s time–frequency track. We do simulations by injecting binary neutron star merger signals in various scenarios where the detector goes through a period of nonstationarity with reference noise curves of third-generation detectors (Cosmic Explorer, the Einstein telescope). As an example, for a source where mismodeling of the noise biases the signal-to-noise estimate by even 10%, one would expect the estimated sky localization to be either under- or overreported by ∼20%; errors like this, especially in low latency, could potentially cause follow-up campaigns to miss the actual source location.
... Here S n (f i ) is defined as power spectral density which is the Fourier transform of the correlation function C(τ ) where τ = |t i − t j | is the time lag. The validity of the assumptions of the noise being Gaussian and stationary can be tested by various techniques, for example, with large number of injections in simulated Gaussian noise and detector data, the percentile-percentile test is done with posterior samples to see if the recovered credible intervals matches with the statistical expectations (Kulkarni & Capano 2021). One can also use the distribution of PSD variation statistic v s to identify the stretches of the data which do not agree with the expected statistical distribution of v s for the Gaussian and stationary noise (Mozzon et al. 2020), or by measuring the noise covariance of the data (Edy et al. 2021). ...
The sensitivity of gravitational-waves detectors is characterized by their noise curves which determine the detector's reach and the ability to accurately measure the parameters of astrophysical sources. The detector noise is typically modelled as stationary and Gaussian for many practical purposes. However, physical changes in the state of detectors due to environmental and instrumental factors, including extreme cases where a detector discontinues observing for some time, introduce non-stationarity into the noise. Even slow evolution of the detector sensitivity will affect long duration signals such as binary neutron star (BNS) mergers. Mis-estimation of the noise behavior directly impacts the posterior width of the signal parameters. This becomes an issue for studies which depend on accurate localization volumes such as i) probing cosmological parameters (such as Hubble constant, clustering bias) using cross-correlation methods with galaxies, ii) doing electromagnetic follow-up using localization information from parameter estimation done from pre-merger data. We study the effects of dynamical noise on the parameter estimation of the GW events. We develop a new method to correct dynamical noise by estimating a locally-valid pseudo PSD which is normalized along the time-frequency track of a potential signal. We do simulations by injecting the BNS signal in various scenarios where the detector goes through a period of non-stationarity with reference noise curve of third generation detectors (Cosmic explorer, Einstein telescope). As an example, for a source where mis-modelling of the noise biases the signal-to-noise estimate by even , one would expect the estimated localization volume to be either under or over reported by ; errors like this, especially in low-latency, could potentially cause follow-up campaigns to miss the true source location.
... This does not always hold in practice due to the finite number of samples and the limitations of MC algorithms. Sampling bias may be an important issue for a broader class of events including GW151226 and GW150914 [50], and in agreement with previous studies [37,38] we find that the standard LVC priors lead to an incomplete map of the GW190521 likelihood manifold. In contrast to previous approaches, we do not assume that any one choice of prior produces samples that can be reweighted reliably. ...
We map the likelihood of GW190521, the heaviest detected binary black hole (BBH) merger, by sampling under different mass and spin priors designed to be uninformative. We find that a source-frame total mass of is consistently supported, but posteriors in mass ratio and spin depend critically on the choice of priors. We confirm that the likelihood has a multi-modal structure with peaks in regions of mass ratio representing very different astrophysical scenarios. The unequal-mass region () has an average likelihood times larger than the equal-mass region () and a maximum likelihood larger. Using ensembles of samples across priors, we examine the implications of qualitatively different BBH sources that fit the data. We find that the equal-mass solution has poorly constrained spins and at least one black hole mass that is difficult to form via stellar collapse due to pair instability. The unequal-mass solution can avoid this mass gap entirely but requires a negative effective spin and a precessing primary. Either of these scenarios is more easily produced by dynamical formation channels than field binary co-evolution. The sensitive comoving volume-time of the mass gap solution is times larger than the gap-avoiding solution. After accounting for this distance effect, the likelihood still reverses the advantage to favor the gap-avoiding scenario by a factor of before considering mass and spin priors. Posteriors are easily driven away from this high-likelihood region by common prior choices meant to be uninformative, making GW190521 parameter inference sensitive to the assumed mass and spin distributions of mergers in the source's astrophysical channel. This may be a generic issue for similarly heavy events given current detector sensitivity and waveform degeneracies.
We map the likelihood of GW190521, the heaviest detected binary black hole (BBH) merger, by sampling under different mass and spin priors designed to be uninformative. We find that a source-frame total mass of ∼150 M⊙ is consistently supported, but posteriors in mass ratio and spin depend critically on the choice of priors. We confirm that the likelihood has a multimodal structure with peaks in regions of mass ratio representing very different astrophysical scenarios. The unequal-mass region (m2/m1<0.3) has an average likelihood ∼e6 times larger than the equal-mass region (m2/m1>0.3) and a maximum likelihood ∼e2 larger. Using ensembles of samples across priors, we examine the implications of qualitatively different BBH sources that fit the data. We find that the equal-mass solution has poorly constrained spins and at least one black hole mass that is difficult to form via stellar collapse due to pair instability. The unequal-mass solution can avoid this mass gap entirely but requires a negative effective spin and a precessing primary. Either of these scenarios is more easily produced by dynamical formation channels than field binary coevolution. Drawing representative samples from each region of the likelihood map, we find a sensitive comoving volume time O(10) times larger in the mass gap region than the gap-avoiding region. Considering Dcom3L to account for the distance effect, the likelihood of these representative samples still reverses the advantage to favor the gap-avoiding scenario by a factor of O(100) before including mass and spin priors. Posteriors are easily driven away from this high-likelihood region by common prior choices meant to be uninformative, making GW190521 parameter inference sensitive to the assumed mass and spin distributions of mergers in the source's astrophysical channel. This may be a generic issue for similarly heavy events given current detector sensitivity and waveform degeneracies.
This paper presents the gravitational-wave measurement of the Hubble constant (H-0) using the detections from the first and second observing runs of the Advanced LIGO and Virgo detector network. The presence of the transient electromagnetic counterpart of the binary neutron star GW170817 led to the first standard-siren measurement of H-0. Here we additionally use binary black hole detections in conjunction with galaxy catalogs and report a joint measurement. Our updated measurement is H-0 = 69(-8)(+16) km s(-1) Mpc(-1) (68.3% of the highest density posterior interval with a flat-in-log prior) which is an improvement by a factor of 1.04 (about 4%) over the GW170817-only value of 69(-8)(+17) km s(-1) Mpc(-1). A significant additional contribution currently comes from GW170814, a loud and well-localized detection from a part of the sky thoroughly covered by the Dark Energy Survey. With numerous detections anticipated over the upcoming years, an exhaustive understanding of other systematic effects are also going to become increasingly important. These results establish the path to cosmology using gravitational-wave observations with and without transient electromagnetic counterparts.
Gravitational waves provide a unique tool for observational astronomy. While the first LIGO--Virgo catalogue of gravitational-wave transients (GWTC-1) contains eleven signals from black hole and neutron star binaries, the number of observations is increasing rapidly as detector sensitivity improves. To extract information from the observed signals, it is imperative to have fast, flexible, and scalable inference techniques. In a previous paper, we introduced BILBY: a modular and user-friendly Bayesian inference library adapted to address the needs of gravitational-wave inference. In this work, we demonstrate that BILBY produces reliable results for simulated gravitational-wave signals from compact binary mergers, and verify that it accurately reproduces results reported for the eleven GWTC-1 signals. Additionally, we provide configuration and output files for all analyses to allow for easy reproduction, modification, and future use. This work establishes that BILBY is primed and ready to analyse the rapidly growing population of compact binary coalescence gravitational-wave signals.
We report the detection of new binary black hole merger events in the publicly available data from the second observing run of Advanced LIGO and Advanced Virgo (O2). The mergers were discovered using the new search pipeline described in Venumadhav et al. [Phys. Rev. D 100, 023011 (2019)] and are above the detection thresholds as defined in Abbott et al. (LIGO Scientific and Virgo Collaborations) [Phys. Rev. X 9, 031040 (2019).]. Three of the mergers (GW170121, GW170304, GW170727) have inferred probabilities of being of astrophysical origin pastro>0.98. The remaining three (GW170425, GW170202, GW170403) are less certain, with pastro ranging from 0.5 to 0.8. The newly found mergers largely share the statistical properties of previously reported events, with the exception of GW170403, the least secure event, which has a highly negative effective spin parameter χeff. The most secure new event, GW170121 (pastro>0.99), is also notable due to its inferred negative value of χeff, which is inconsistent with being positive at the ≈95.8% confidence level. The new mergers nearly double the sample of gravitational wave events reported from O2 and present a substantial opportunity to explore the statistics of the binary black hole population in the Universe. The number of detected events is not surprising since we estimate that the detection volume of our pipeline may be larger than that of other pipelines by as much as a factor of 2 (with significant uncertainties in the estimate). The increase in volume is larger when the constituent detectors of the network have very different sensitivities, as is likely to be the case in current and future runs.
Advanced LIGO and Advanced Virgo are actively monitoring the sky and collecting gravitational-wave strain data with sufficient sensitivity to detect signals routinely. In this paper we describe the data recorded by these instruments during their first and second observing runs. The main data products are the gravitational-wave strain arrays, released as time series sampled at 16384 Hz. The datasets that include this strain measurement can be freely accessed through the Gravitational Wave Open Science Center at this http URL, together with data-quality information essential for the analysis of LIGO and Virgo data, documentation, tutorials, and supporting software.
We present the second Open Gravitational-wave Catalog (2-OGC) of compact-binary coalescences, obtained from the complete set of public data from Advanced LIGO’s first and second observing runs. For the first time we also search public data from the Virgo observatory. The sensitivity of our search benefits from updated methods of ranking candidate events including the effects of nonstationary detector noise and varying network sensitivity; in a separate targeted binary black hole merger search we also impose a prior distribution of binary component masses. We identify a population of 14 binary black hole merger events with probability of astrophysical origin >0.5 as well as the binary neutron star merger GW170817. We confirm the previously reported events GW170121, GW170304, and GW170727 and also report GW151205, a new marginal binary black hole merger with a primary mass of that may have formed through hierarchical merger. We find no additional significant binary neutron star merger or neutron star–black hole merger events. To enable deeper follow-up as our understanding of the underlying populations evolves, we make available our comprehensive catalog of events, including the subthreshold population of candidates and posterior samples from parameter inference of the 30 most significant binary black hole candidates.
The properties of neutron stars are determined by the nature of the matter that they contain. These properties can be constrained by measurements of the star’s size. We obtain stringent constraints on neutron-star radii by combining multimessenger observations of the binary neutron-star merger GW170817 with nuclear theory that best accounts for density-dependent uncertainties in the equation of state. We construct equations of state constrained by chiral effective field theory and marginalize over these using the gravitational-wave observations. Combining this with the electromagnetic observations of the merger remnant that imply the presence of a short-lived hypermassive neutron star, we find that the radius of a 1.4 M⊙ neutron star is R1.4M⊙=11.0−0.6+0.9km (90% credible interval). Using this constraint, we show that neutron stars are unlikely to be disrupted in neutron star–black hole mergers; subsequently, such events will not produce observable electromagnetic emission. The combination of electromagnetic and gravitational-wave observations of binary neutron-star merger GW170817 with systematic sets of neutron-star equations of state has produced a tightly constrained radius of 11 km for a 1.4 M⊙ neutron star. This constraint suggests that a neutron star–black hole merger is unlikely to produce an electromagnetic counterpart.
We present the results from three gravitational-wave searches for coalescing compact binaries with component masses above 1 M ⊙ during the first and second observing runs of the advanced gravitational-wave detector network. During the first observing run ( O 1 ), from September 12, 2015 to January 19, 2016, gravitational waves from three binary black hole mergers were detected. The second observing run ( O 2 ), which ran from November 30, 2016 to August 25, 2017, saw the first detection of gravitational waves from a binary neutron star inspiral, in addition to the observation of gravitational waves from a total of seven binary black hole mergers, four of which we report here for the first time: GW170729, GW170809, GW170818, and GW170823. For all significant gravitational-wave events, we provide estimates of the source properties. The detected binary black holes have total masses between 18.6 − 0.7 + 3.2 M ⊙ and 84.4 − 11.1 + 15.8 M ⊙ and range in distance between 320 − 110 + 120 and 2840 − 1360 + 1400 Mpc . No neutron star–black hole mergers were detected. In addition to highly significant gravitational-wave events, we also provide a list of marginal event candidates with an estimated false-alarm rate less than 1 per 30 days. From these results over the first two observing runs, which include approximately one gravitational-wave detection per 15 days of data searched, we infer merger rates at the 90% confidence intervals of 110 − 3840 Gpc − 3 y − 1 for binary neutron stars and 9.7 − 101 Gpc − 3 y − 1 for binary black holes assuming fixed population distributions and determine a neutron star–black hole merger rate 90% upper limit of 610 Gpc − 3 y − 1 .
Published by the American Physical Society 2019
Blip glitches are short noise transients present in data from ground-based gravitational-wave observatories. These glitches resemble the gravitational-wave signature of massive binary black hole mergers. Hence, the sensitivity of transient gravitational-wave searches to such high-mass systems and other potential short duration sources is degraded by the presence of blip glitches. The origin and rate of occurrence of this type of glitch have been largely unknown. In this paper we explore the population of blip glitches in Advanced LIGO during its first and second observing runs. On average, we find that Advanced LIGO data contains approximately two blip glitches per hour of data. We identify four subsets of blip glitches correlated with detector auxiliary or environmental sensor channels, however the physical causes of the majority of blips remain unclear.
We present the first Open Gravitational-wave Catalog, obtained by using the public data from Advanced LIGO's first observing run to search for compact-object binary mergers. Our analysis is based on new methods that improve the separation between signals and noise in matched-filter searches for gravitational waves from the merger of compact objects. The three most significant signals in our catalog correspond to the binary black hole mergers GW150914, GW151226, and LVT151012. We assume a common population of binary black holes for these three signals by defining a region of parameter space that is consistent with these events. Under this assumption, we find that LVT151012 has a 97.6% probability of being astrophysical in origin. No other significant binary black hole candidates are found, nor did we observe any significant binary neutron star or neutron star–black hole candidates. We make available our complete catalog of events, including the subthreshold population of candidates.
The first observing run of Advanced LIGO spanned 4 months, from 12 September 2015 to 19 January 2016, during which gravitational waves were directly detected from two binary black hole systems, namely GW150914 and GW151226. Confident detection of gravitational waves requires an understanding of instrumental transients and artifacts that can reduce the sensitivity of a search. Studies of the quality of the detector data yield insights into the cause of instrumental artifacts and data quality vetoes specific to a search are produced to mitigate the effects of problematic data. In this paper, the systematic removal of noisy data from analysis time is shown to improve the sensitivity of searches for compact binary coalescences. The output of the PyCBC pipeline, which is a python-based code package used to search for gravitational wave signals from compact binary coalescences, is used as a metric for improvement. GW150914 was a loud enough signal that removing noisy data did not improve its significance. However, the removal of data with excess noise decreased the false alarm rate of GW151226 by more than two orders of magnitude, from 1 in 770 yr to less than 1 in 186 000 yr.
On August 17, 2017 at 12∶41:04 UTC the Advanced LIGO and Advanced Virgo gravitational-wave detectors made their first observation of a binary neutron star inspiral. The signal, GW170817, was detected with a combined signal-to-noise ratio of 32.4 and a false-alarm-rate estimate of less than one per 8.0 × 10 4 years . We infer the component masses of the binary to be between 0.86 and 2.26 M ⊙ , in agreement with masses of known neutron stars. Restricting the component spins to the range inferred in binary neutron stars, we find the component masses to be in the range 1.17 – 1.60 M ⊙ , with the total mass of the system 2.7 4 − 0.01 + 0.04 M ⊙ . The source was localized within a sky region of 28 deg 2 (90% probability) and had a luminosity distance of 4 0 − 14 + 8 Mpc , the closest and most precisely localized gravitational-wave signal yet. The association with the γ -ray burst GRB 170817A, detected by Fermi-GBM 1.7 s after the coalescence, corroborates the hypothesis of a neutron star merger and provides the first direct evidence of a link between these mergers and short γ -ray bursts. Subsequent identification of transient counterparts across the electromagnetic spectrum in the same location further supports the interpretation of this event as a neutron star merger. This unprecedented joint gravitational and electromagnetic observation provides insight into astrophysics, dense matter, gravitation, and cosmology.
Published by the American Physical Society 2017
On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg² at a luminosity distance of Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 . An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ) less than 11 hours after the merger by the One-Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient's position and days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC 4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta.
The detection of GW170817 (ref. 1) heralds the age of gravitational-wave multi-messenger astronomy, with the observations of gravitational-wave and electromagnetic emission from the same transient source. On 17 August 2017 the network of Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) and Virgo detectors observed GW170817, a strong signal from the merger of a binary neutron-star system. Less than two seconds after the merger, a γ-ray burst event, GRB 170817A, was detected consistent with the LIGO–Virgo sky localization region). The sky region was subsequently observed by optical astronomy facilities, resulting in the identification of an optical transient signal within about 10 arcseconds of the galaxy NGC 4993 (refs 8–13). GW170817 can be used as a standard siren, combining the distance inferred purely from the gravitational-wave signal with the recession velocity arising from the electromagnetic data to determine the Hubble constant. This quantity, representing the local expansion rate of the Universe, sets the overall scale of the Universe and is of fundamental importance to cosmology. Our measurements do not require any form of cosmic ‘distance ladder’; the gravitational-wave analysis directly estimates the luminosity distance out to cosmological scales. Here we report H_0 = 70.0^(+12.0)_(-8.0) kilometres per second per megaparsec, which is consistent with existing measurements, while being completely independent of them.
We present an improved search for binary compact-object mergers using a network of ground-based gravitational-wave detectors. We model a volumetric, isotropic source population and incorporate the resulting distribution over signal amplitude, time delay, and coalescence phase into the ranking of candidate events. We describe an improved modeling of the background distribution, and demonstrate incorporating a prior model of the binary mass distribution in the ranking of candidate events. We find a and increase in detection volume for simulated binary neutron star and neutron star--binary black hole systems, respectively, corresponding to a reduction of the false alarm rates assigned to signals by between one and two orders of magnitude.
We describe the PyCBC search for gravitational waves from compact-object binary coalescences in advanced gravitational-wave detector data. The search was used in the first Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) observing run and unambiguously identified two black hole binary mergers, GW150914 and GW151226. At its core, the PyCBC search performs a matched-filter search for binary merger signals using a bank of gravitational-wave template waveforms. We provide a complete description of the search pipeline including the steps used to mitigate the effects of noise transients in the data, identify candidate events and measure their statistical significance. The analysis is able to measure false-alarm rates as low as one per million years, required for confident detection of signals. Using data from initial LIGOs sixth science run, we show that the new analysis reduces the background noise in the search, giving a 30% increase in sensitive volume for binary neutron star systems over previous searches.
We report the observation of a gravitational-wave signal produced by the coalescence of two stellar-mass black holes. The signal, GW151226, was observed by the twin detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) on December 26, 2015 at 03:38:53 UTC. The signal was initially identified within 70 s by an online matched-filter search targeting binary coalescences. Subsequent off-line analyses recovered GW151226 with a network signal-to-noise ratio of 13 and a significance greater than 5 σ . The signal persisted in the LIGO frequency band for approximately 1 s, increasing in frequency and amplitude over about 55 cycles from 35 to 450 Hz, and reached a peak gravitational strain of 3. 4 − 0.9 + 0.7 × 10 − 22 . The inferred source-frame initial black hole masses are 14.2 − 3.7 + 8.3 M ⊙ and 7. 5 − 2.3 + 2.3 M ⊙ , and the final black hole mass is 20.8 − 1.7 + 6.1 M ⊙ . We find that at least one of the component black holes has spin greater than 0.2. This source is located at a luminosity distance of 44 0 − 190 + 180 Mpc corresponding to a redshift of 0.0 9 − 0.04 + 0.03 . All uncertainties define a 90% credible interval. This second gravitational-wave observation provides improved constraints on stellar populations and on deviations from general relativity.
Published by the American Physical Society 2016
The first observational run of the Advanced LIGO detectors, from September 12, 2015 to January 19, 2016, saw the first detections of gravitational waves from binary black hole mergers. In this paper, we present full results from a search for binary black hole merger signals with total masses up to 100 M ⊙ and detailed implications from our observations of these systems. Our search, based on general-relativistic models of gravitational-wave signals from binary black hole systems, unambiguously identified two signals, GW150914 and GW151226, with a significance of greater than 5 σ over the observing period. It also identified a third possible signal, LVT151012, with substantially lower significance and with an 87% probability of being of astrophysical origin. We provide detailed estimates of the parameters of the observed systems. Both GW150914 and GW151226 provide an unprecedented opportunity to study the two-body motion of a compact-object binary in the large velocity, highly nonlinear regime. We do not observe any deviations from general relativity, and we place improved empirical bounds on several high-order post-Newtonian coefficients. From our observations, we infer stellar-mass binary black hole merger rates lying in the range 9 – 240 Gpc − 3 yr − 1 . These observations are beginning to inform astrophysical predictions of binary black hole formation rates and indicate that future observing runs of the Advanced detector network will yield many more gravitational-wave detections.
Published by the American Physical Society 2016
On 14 September 2015, a gravitational wave signal from a coalescing black hole binary system was observed by the Advanced LIGO detectors. This paper describes the transient noise backgrounds used to determine the significance of the event (designated GW150914) and presents the results of investigations into potential correlated or uncorrelated sources of transient noise in the detectors around the time of the event. The detectors were operating nominally at the time of GW150914. We have ruled out environmental influences and non-Gaussian instrument noise at either LIGO detector as the cause of the observed gravitational wave signal.
On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0 × 10 − 21 . It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1 σ . The source lies at a luminosity distance of 41 0 − 180 + 160 Mpc corresponding to a redshift z = 0.0 9 − 0.04 + 0.03 . In the source frame, the initial black hole masses are 3 6 − 4 + 5 M ⊙ and 2 9 − 4 + 4 M ⊙ , and the final black hole mass is 6 2 − 4 + 4 M ⊙ , with 3. 0 − 0.5 + 0.5 M ⊙ c 2 radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.
Published by the American Physical Society 2016
The Advanced Laser Interferometer Gravitational-wave Observatory (LIGO)
detectors have completed their initial upgrade phase and will enter the first
observing run in late 2015, with detector sensitivity expected to improve in
future runs. Through the combined efforts of on-site commissioners and the
Detector Characterization group of the LIGO Scientific Collaboration,
interferometer performance, in terms of data quality, at both LIGO
observatories has vastly improved from the start of commissioning efforts to
present. Advanced LIGO has already surpassed Enhanced LIGO in sensitivity, and
the rate of noise transients, which would negatively impact astrophysical
searches, has improved. Here we give details of some of the work which has
taken place to better the quality of the LIGO data ahead of the first observing
run.
The Advanced LIGO gravitational wave detectors are second-generation instruments designed and built for the two LIGO observatories in Hanford, WA and Livingston, LA, USA. The two instruments are identical in design, and are specialized versions of a Michelson interferometer with 4 km long arms. As in Initial LIGO, Fabry–Perot cavities are used in the arms to increase the interaction time with a gravitational wave, and power recycling is used to increase the effective laser power. Signal recycling has been added in Advanced LIGO to improve the frequency response. In the most sensitive frequency region around 100 Hz, the design strain sensitivity is a factor of 10 better than Initial LIGO. In addition, the low frequency end of the sensitivity band is moved from 40 Hz down to 10 Hz. All interferometer components have been replaced with improved technologies to achieve this sensitivity gain. Much better seismic isolation and test mass suspensions are responsible for the gains at lower frequencies. Higher laser power, larger test masses and improved mirror coatings lead to the improved sensitivity at mid and high frequencies. Data collecting runs with these new instruments are planned to begin in mid-2015.
Advanced ground-based gravitational-wave (GW) detectors begin operation
imminently. Their intended goal is not only to make the first direct detection
of GWs, but also to make inferences about the source systems. Binary
neutron-star mergers are among the most promising sources. We investigate the
performance of the parameter-estimation pipeline that will be used during the
first observing run of the Advanced Laser Interferometer Gravitational-wave
Observatory (aLIGO) in 2015: we concentrate on the ability to reconstruct the
source location on the sky, but also consider the ability to measure masses and
the distance. Accurate, rapid sky-localization is necessary to alert
electromagnetic (EM) observatories so that they can perform follow-up searches
for counterpart transient events. We consider parameter-estimation accuracy in
the presence of realistic, non-Gaussian noise. We find that the character of
the noise makes negligible difference to the parameter-estimation performance.
The source luminosity distance can only be poorly constrained, the median
() credible interval scaled with respect to the true distance is
0.85 (0.38). However, the chirp mass is well measured. Our chirp-mass
estimates are subject to systematic error because we used
gravitational-waveform templates without component spin to carry out inference
on signals with moderate spins, but the total error is typically less than
. The median () credible region for sky
localization is (), with
() of detected events localized within .
Early aLIGO, with only two detectors, will have a sky-localization accuracy for
binary neutron stars of hundreds of square degrees; this makes EM follow-up
challenging, but not impossible.
A central challenge in Gravitational Wave Astronomy is identifying weak
signals in the presence of non-stationary and non-Gaussian noise. The
separation of gravitational wave signals from noise requires good models for
both. When accurate signal models are available, such as for binary Neutron
star systems, it is possible to make robust detection statements even when the
noise is poorly understood. In contrast, searches for "un-modeled" transient
signals are strongly impacted by the methods used to characterize the noise.
Here we take a Bayesian approach and introduce a multi-component, variable
dimension, parameterized noise model that explicitly accounts for
non-stationarity and non-Gaussianity in data from interferometric gravitational
wave detectors. Instrumental transients (glitches) and burst sources of
gravitational waves are modeled using a Morlet-Gabor continuous wavelet basis.
The number and placement of the wavelets is determined by a trans-dimensional
Reversible Jump Markov Chain Monte Carlo algorithm. The Gaussian component of
the noise and sharp line features in the noise spectrum are modeled using the
BayesLine algorithm, which operates in concert with the wavelet model.
The Advanced LIGO and Advanced Virgo gravitational wave (GW) detectors will
begin operation in the coming years, with compact binary coalescence events a
likely source for the first detections. The gravitational waveforms emitted
directly encode information about the sources, including the masses and spins
of the compact objects. Recovering the physical parameters of the sources from
the GW observations is a key analysis task. This work describes the
LALInference software library for Bayesian parameter estimation of compact
binary coalescence (CBC) signals, which builds on several previous methods to
provide a well-tested toolkit which has already been used for several studies.
We are able to show using three independent sampling algorithms that our
implementation consistently converges on the same results, giving confidence in
the parameter estimates thus obtained.
We demonstrate this with a detailed comparison on three compact binary
systems: a binary neutron star, a neutron star-black hole binary and a binary
black hole, where we show a cross-comparison of results. These systems were
analysed with non-spinning, aligned spin and generic spin configurations
respectively, showing that consistent results can be obtained even with the
full 15-dimensional parameter space of the generic spin configurations. We also
demonstrate statistically that the Bayesian credible intervals we recover
correspond to frequentist confidence intervals under correct prior assumptions
by analysing a set of 100 signals drawn from the prior.
We discuss the computational cost of these algorithms, and describe the
general and problem-specific sampling techniques we have used to improve the
efficiency of sampling the CBC parameter space.
Advanced Virgo is the project to upgrade the Virgo interferometric detector
of gravitational waves, with the aim of increasing the number of observable
galaxies (and thus the detection rate) by three orders of magnitude. The
project is now in an advanced construction phase and the assembly and
integration will be completed by the end of 2015. Advanced Virgo will be part
of a network with the two Advanced LIGO detectors in the US and GEO HF in
Germany, with the goal of contributing to the early detections of gravitational
waves and to opening a new observation window on the universe. In this paper we
describe the main features of the Advanced Virgo detector and outline the
status of the construction.
emcee is an extensible, pure-Python implementation of Goodman &
Weare's Affine Invariant Markov chain Monte Carlo (MCMC) Ensemble
sampler. It's designed for Bayesian parameter estimation. The algorithm
behind emcee has several advantages over traditional MCMC sampling
methods and has excellent performance as measured by the autocorrelation
time (or function calls per independent sample). One advantage of the
algorithm is that it requires hand-tuning of only 1 or 2 parameters
compared to ˜ N^2 for a traditional algorithm in an N-dimensional
parameter space. Exploiting the parallelism of the ensemble method,
emcee permits any user to take advantage of multiple CPU cores without
extra effort.
The problem of reconstructing the sky position of compact binary coalescences
detected via gravitational waves is a central one for future observations with
the ground-based network of gravitational-wave laser interferometers, such as
Advanced LIGO and Advanced Virgo. Different techniques for sky localisation
have been independently developed. They can be divided in two broad categories:
fully coherent Bayesian techniques, which are high-latency and aimed at
in-depth studies of all the parameters of a source, including sky position, and
"triangulation-based" techniques, which exploit the data products from the
search stage of the analysis to provide an almost real-time approximation of
the posterior probability density function of the sky location of a detection
candidate. These techniques have previously been applied to data collected
during the last science runs of gravitational-wave detectors operating in the
so-called initial configuration.
Here, we develop and analyse methods for assessing the self-consistency of
parameter estimation methods and carrying out fair comparisons between
different algorithms, addressing issues of efficiency and optimality. These
methods are general, and can be applied to parameter estimation problems other
than sky localisation. We apply these methods to two existing sky localisation
techniques representing the two above-mentioned categories, using a set of
simulated inspiral-only signals from compact binary systems with total mass
and non-spinning components. We compare the relative
advantages and costs of the two techniques and show that sky location
uncertainties are on average a factor smaller for fully coherent
techniques than for the specific variant of the "triangulation-based" technique
used during the last science runs, at the expense of a factor
longer processing time.
The construction of a model of the gravitational-wave (GW) signal from
generic configurations of spinning-black-hole binaries, through inspiral,
merger and ringdown, is one of the most pressing theoretical problems in the
build-up to the era of GW astronomy. We present such a model, "PhenomP", which
captures the basic phenomenology of the seven-dimensional parameter space of
binary configurations with only three physical parameters. Essentially, we
simply "twist up" a two-parameter non-precessing-binary model with approximate
expressions for the precessional motion, which require only one additional
physical parameter, an effective precession spin. The model is constructed in
the frequency domain, which will be essential for efficient GW searches and
source measurements. We have tested the model's fidelity for GW applications by
comparison against hybrid post-Newtonian-numerical-relativity waveforms at a
variety of configurations - although we did not use these numerical simulations
in the construction of the model. Our model can be used to develop GW searches,
to study the implications for astrophysical measurements, and, perhaps most
importantly, as a simple conceptual framework to form the basis of
generic-binary waveform modelling in the advanced-detector era.
Searches for known waveforms in gravitational wave detector data are often done using matched filtering. When used on real instrumental data, matched filtering often does not perform as well as might be expected, because non-stationary and non-Gaussian detector noise produces large spurious filter outputs (events). This paper describes a χ 2 time-frequency test which is one way to discrimi-nate such spurious events from the events that would be produced by genuine signals. The method works well only for broad-band signals. The case where the filter template does not exactly match the signal waveform is also considered, and upper bounds are found for the expected value of χ 2 .
Matched-filter searches for gravitational waves from coalescing compact
binaries by the LIGO Scientific Collaboration use the findchirp algorithm: an
implementation of the optimal filter with innovations to account for unknown
signal parameters and to improve performance on detector data that has
non-stationary and non-Gaussian artifacts. We provide details on the methods
used in the findchirp algorithm as used in the search for sub-solar mass
binaries, binary neutron stars, neutron star--black hole binaries and binary
black holes.
Significant human and observational resources have been dedicated to electromagnetic follow-up of gravitational-wave events detected by Advanced LIGO and Virgo. As the sensitivity of LIGO and Virgo improves, the rate of sources detected will increase. Margalit & Metzger (2019) have suggested that it may be necessary to prioritize observations of future events. Optimal prioritization requires a rapid measurement of a gravitational-wave event’s masses and spins, as these can determine the nature of any electromagnetic emission. We extend the relative binning method of Cornish (2013) and Zackay et al. (2018) to a coherent detector-network statistic. We show that the method can be seeded from the output of a matched-filter search and used in a Bayesian parameter measurement framework to produce marginalized posterior probability densities for the source’s parameters within 20 minutes of detection on 32 CPU cores. We demonstrate that this algorithm produces unbiased estimates of the parameters with the same accuracy as running parameter estimation using the standard gravitational-wave likelihood. We encourage the adoption of this method in future LIGO–Virgo observing runs to allow fast dissemination of the parameters of detected events so that the observing community can make best use of its resources.
Understanding the properties of transient gravitational waves (GWs) and their sources is of broad interest in physics and astronomy. Bayesian inference is the standard framework for astrophysical measurement in transient GW astronomy. Usually, stochastic sampling algorithms are used to estimate posterior probability distributions over the parameter spaces of models describing experimental data. The most physically accurate models typically come with a large computational overhead which can render data analsis extremely time consuming, or possibly even prohibitive. In some cases highly specialized optimizations can mitigate these issues, though they can be difficult to implement, as well as to generalize to arbitrary models of the data. Here, we investigate an accurate, flexible, and scalable method for astrophysical inference: parallelized nested sampling. The reduction in the wall-time of inference scales almost linearly with the number of parallel processes running on a high-performance computing cluster. By utilizing a pool of several hundreds or thousands of CPUs in a high-performance cluster, the large wall times of many astrophysical inferences can be alleviated while simultaneously ensuring that any GW signal model can be used ‘out of the box’, i.e. without additional optimization or approximation. Our method will be useful to both the LIGO-Virgo-KAGRA collaborations and the wider scientific community performing astrophysical analyses on GWs. An implementation is available in the open source gravitational-wave inference library pBilby (parallel bilby).
We present dynesty, a public, open-source, python package to estimate Bayesian posteriors and evidences (marginal likelihoods) using the dynamic nested sampling methods developed by Higson et al. By adaptively allocating samples based on posterior structure, dynamic nested sampling has the benefits of Markov chain Monte Carlo (MCMC) algorithms that focus exclusively on posterior estimation while retaining nested sampling’s ability to estimate evidences and sample from complex, multimodal distributions. We provide an overview of nested sampling, its extension to dynamic nested sampling, the algorithmic challenges involved, and the various approaches taken to solve them in this and previous work. We then examine dynesty’s performance on a variety of toy problems along with several astronomical applications. We find in particular problems dynesty can provide substantial improvements in sampling efficiency compared to popular MCMC approaches in the astronomical literature. More detailed statistical results related to nested sampling are also included in the appendix.
The detection of gravitational waves by Advanced LIGO and Advanced Virgo provides an opportunity to test general relativity in a regime that is inaccessible to traditional astronomical observations and laboratory tests. We present four tests of the consistency of the data with binary black hole gravitational waveforms predicted by general relativity. One test subtracts the best-fit waveform from the data and checks the consistency of the residual with detector noise. The second test checks the consistency of the low- and high-frequency parts of the observed signals. The third test checks that phenomenological deviations introduced in the waveform model (including in the post-Newtonian coefficients) are consistent with 0. The fourth test constrains modifications to the propagation of gravitational waves due to a modified dispersion relation, including that from a massive graviton. We present results both for individual events and also results obtained by combining together particularly strong events from the first and second observing runs of Advanced LIGO and Advanced Virgo, as collected in the catalog GWTC-1. We do not find any inconsistency of the data with the predictions of general relativity and improve our previously presented combined constraints by factors of 1.1 to 2.5. In particular, we bound the mass of the graviton to be mg≤4.7×10−23 eV/c2 (90% credible level), an improvement of a factor of 1.6 over our previously presented results. Additionally, we check that the four gravitational-wave events published for the first time in GWTC-1 do not lead to stronger constraints on alternative polarizations than those published previously.
The recent discovery by Advanced LIGO and Advanced Virgo of a gravitational wave signal from a binary neutron star inspiral has enabled tests of general relativity (GR) with this new type of source. This source, for the first time, permits tests of strong-field dynamics of compact binaries in the presence of matter. In this Letter, we place constraints on the dipole radiation and possible deviations from GR in the post-Newtonian coefficients that govern the inspiral regime. Bounds on modified dispersion of gravitational waves are obtained; in combination with information from the observed electromagnetic counterpart we can also constrain effects due to large extra dimensions. Finally, the polarization content of the gravitational wave signal is studied. The results of all tests performed here show good agreement with GR.
We introduce new modules in the open-source PyCBC gravitational-wave astronomy toolkit that implement Bayesian inference for compact-object binary mergers. We review the Bayesian inference methods implemented and describe the structure of the modules. We demonstrate that the PyCBC Inference modules produce unbiased estimates of the parameters of a simulated population of binary black hole mergers. We show that the parameters’ posterior distributions obtained using our new code agree well with the published estimates for binary black holes in the first Advanced LIGO–Virgo observing run. © 2019. The Astronomical Society of the Pacific. All rights reserved.
DOI:https://doi.org/10.1103/PhysRevLett.121.259902
On 17 August 2017, the LIGO and Virgo observatories made the first direct detection of gravitational waves from the coalescence of a neutron star binary system. The detection of this gravitational-wave signal, GW170817, offers a novel opportunity to directly probe the properties of matter at the extreme conditions found in the interior of these stars. The initial, minimal-assumption analysis of the LIGO and Virgo data placed constraints on the tidal effects of the coalescing bodies, which were then translated to constraints on neutron star radii. Here, we expand upon previous analyses by working under the hypothesis that both bodies were neutron stars that are described by the same equation of state and have spins within the range observed in Galactic binary neutron stars. Our analysis employs two methods: the use of equation-of-state-insensitive relations between various macroscopic properties of the neutron stars and the use of an efficient parametrization of the defining function p(ρ) of the equation of state itself. From the LIGO and Virgo data alone and the first method, we measure the two neutron star radii as R1=10.8−1.7+2.0 km for the heavier star and R2=10.7−1.5+2.1 km for the lighter star at the 90% credible level. If we additionally require that the equation of state supports neutron stars with masses larger than 1.97 M⊙ as required from electromagnetic observations and employ the equation-of-state parametrization, we further constrain R1=11.9−1.4+1.4 km and R2=11.9−1.4+1.4 km at the 90% credible level. Finally, we obtain constraints on p(ρ) at supranuclear densities, with pressure at twice nuclear saturation density measured at 3.5−1.7+2.7×1034 dyn cm−2 at the 90% level.
In the coming years gravitational-wave detectors will undergo a series of improvements, with an increase in their detection rate by about an order of magnitude. Routine detections of gravitational-wave signals promote novel astrophysical and fundamental theory studies, while simultaneously leading to an increase in the number of detections temporally overlapping with instrumentally- or environmentally-induced transients in the detectors (glitches), often of unknown origin. Indeed, this was the case for the very first detection by the LIGO and Virgo detectors of a gravitational-wave signal consistent with a binary neutron star coalescence, GW170817. A loud glitch in the LIGO-Livingston detector, about one second before the merger, hampered coincident detection (which was initially achieved solely with LIGO-Hanford data). Moreover, accurate source characterization depends on specific assumptions about the behavior of the detector noise that are rendered invalid by the presence of glitches. In this paper, we present the various techniques employed for the initial mitigation of the glitch to perform source characterization of GW170817 and study advantages and disadvantages of each mitigation method. We show that, despite the presence of instrumental noise transients louder than the one affecting GW170817, we are still able to produce unbiased measurements of the intrinsic parameters from simulated injections with properties similar to GW170817.
This corrects the article DOI: 10.1103/PhysRevLett.116.221101.
We use gravitational-wave observations of the binary neutron star merger GW170817 to explore the tidal deformabilities and radii of neutron stars. We perform a Bayesian parameter estimation with the source location and distance informed by electromagnetic observations. We also assume that the two stars have the same equation of state; we demonstrate that, for stars with masses comparable to the component masses of GW170817, this is effectively implemented by assuming that the stars’ dimensionless tidal deformabilities are determined by the binary’s mass ratio q by Λ1/Λ2=q6. We investigate different choices of prior on the component masses of the neutron stars. We find that the tidal deformability and 90% credible interval is Λ˜=222−138+420 for a uniform component mass prior, Λ˜=245−151+453 for a component mass prior informed by radio observations of Galactic double neutron stars, and Λ˜=233−144+448 for a component mass prior informed by radio pulsars. We find a robust measurement of the common areal radius of the neutron stars across all mass priors of 8.9≤R^≤13.2 km, with a mean value of ⟨R^⟩=10.8 km. Our results are the first measurement of tidal deformability with a physical constraint on the star’s equation of state and place the first lower bounds on the deformability and areal radii of neutron stars using gravitational waves.
This paper presents cosmological results based on full-mission Planck observations of temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation. Our results are in very good agreement with the 2013 analysis of the Planck nominal-mission temperature data, but with increased precision. The temperature and polarization power spectra are consistent with the standard spatially-flat 6-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations (denoted "base ΛCDM" in this paper). From the Planck temperature data combined with Planck lensing, for this cosmology we find a Hubble constant, H0 = (67.8 ± 0.9) km s⁻¹Mpc⁻¹, a matter density parameter Ωm = 0.308 ± 0.012, and a tilted scalar spectral index with ns = 0.968 ± 0.006, consistent with the 2013 analysis. Note that in this abstract we quote 68% confidence limits on measured parameters and 95% upper limits on other parameters. We present the first results of polarization measurements with the Low Frequency Instrument at large angular scales. Combined with the Planck temperature and lensing data, these measurements give a reionization optical depth of τ = 0.066 ± 0.016, corresponding to a reionization redshift of \hbox{}. These results are consistent with those from WMAP polarization measurements cleaned for dust emission using 353-GHz polarization maps from the High Frequency Instrument. We find no evidence for any departure from base ΛCDM in the neutrino sector of the theory; for example, combining Planck observations with other astrophysical data we find Neff = 3.15 ± 0.23 for the effective number of relativistic degrees of freedom, consistent with the value Neff = 3.046 of the Standard Model of particle physics. The sum of neutrino masses is constrained to â'mν < 0.23 eV. The spatial curvature of our Universe is found to be very close to zero, with | ΩK | < 0.005. Adding a tensor component as a single-parameter extension to base ΛCDM we find an upper limit on the tensor-to-scalar ratio of r0.002< 0.11, consistent with the Planck 2013 results and consistent with the B-mode polarization constraints from a joint analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP B-mode data to our analysis leads to a tighter constraint of r0.002 < 0.09 and disfavours inflationarymodels with a V(φ) φ² potential. The addition of Planck polarization data leads to strong constraints on deviations from a purely adiabatic spectrum of fluctuations. We find no evidence for any contribution from isocurvature perturbations or from cosmic defects. Combining Planck data with other astrophysical data, including Type Ia supernovae, the equation of state of dark energy is constrained to w =-1.006 ± 0.045, consistent with the expected value for a cosmological constant. The standard big bang nucleosynthesis predictions for the helium and deuterium abundances for the best-fit Planck base ΛCDM cosmology are in excellent agreement with observations. We also constraints on annihilating dark matter and on possible deviations from the standard recombination history. In neither case do we find no evidence for new physics. The Planck results for base ΛCDM are in good agreement with baryon acoustic oscillation data and with the JLA sample of Type Ia supernovae. However, as in the 2013 analysis, the amplitude of the fluctuation spectrum is found to be higher than inferred from some analyses of rich cluster counts and weak gravitational lensing. We show that these tensions cannot easily be resolved with simple modifications of the base ΛCDM cosmology. Apart from these tensions, the base ΛCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.
The LIGO detection of GW150914 provides an unprecedented opportunity to study the two-body motion of a compact-object binary in the large-velocity, highly nonlinear regime, and to witness the final merger of the binary and the excitation of uniquely relativistic modes of the gravitational field. We carry out several investigations to determine whether GW150914 is consistent with a binary black-hole merger in general relativity. We find that the final remnant's mass and spin, as determined from the low-frequency (inspiral) and high-frequency (postinspiral) phases of the signal, are mutually consistent with the binary black-hole solution in general relativity. Furthermore, the data following the peak of GW150914 are consistent with the least-damped quasinormal mode inferred from the mass and spin of the remnant black hole. By using waveform models that allow for parametrized general-relativity violations during the inspiral and merger phases, we perform quantitative tests on the gravitational-wave phase in the dynamical regime and we determine the first empirical bounds on several high-order post-Newtonian coefficients. We constrain the graviton Compton wavelength, assuming that gravitons are dispersed in vacuum in the same way as particles with mass, obtaining a 90%-confidence lower bound of 10^{13} km. In conclusion, within our statistical uncertainties, we find no evidence for violations of general relativity in the genuinely strong-field regime of gravity.
Modern problems in astronomical Bayesian inference require efficient methods
for sampling from complex, high-dimensional, often multi-modal probability
distributions. Most popular methods, such as Markov chain Monte Carlo sampling,
perform poorly on strongly multi-modal probability distributions, rarely
jumping between modes or settling on just one mode without finding others.
Parallel tempering addresses this problem by sampling simultaneously with
separate Markov chains from tempered versions of the target distribution with
reduced contrast levels. Gaps between modes can be traversed at higher
temperatures, while individual modes can be efficiently explored at lower
temperatures. In this paper, we investigate how one might choose the ladder of
temperatures to achieve lower autocorrelation time for the sampler (and
therefore more efficient sampling). In particular, we present a simple,
easily-implemented algorithm for dynamically adapting the temperature
configuration of a sampler while sampling in order to maximise its efficiency.
This algorithm dynamically adjusts the temperature spacing to achieve a uniform
rate of exchanges between neighbouring temperatures. We compare the algorithm
to conventional geometric temperature configurations on a number of test
distributions, and report efficiency gains by a factor of 1.2--2.5 over a
well-chosen geometric temperature configuration and by a factor of 1.5--5 over
a poorly chosen configuration. On all of these test distributions a sampler
using the dynamical adaptations to achieve uniform acceptance ratios between
neighbouring chains outperforms one that does not.
Gravitational waves (GWs) emitted by generic black-hole binaries show a rich
structure that directly reflects the complex dynamics introduced by the
precession of the orbital plane, which poses a real challenge to the
development of generic waveform models. Recent progress in modelling these
signals relies on an approximate decoupling between the non-precessing secular
inspiral and a precession-induced rotation. However, the latter depends in
general on all physical parameters of the binary which makes modelling efforts
as well as understanding parameter-estimation prospects prohibitively complex.
Here we show that the dominant precession effects can be captured by a reduced
set of spin parameters. Specifically, we introduce a single \emph{effective
precession spin} parameter, , which is defined from the spin components
that lie in the orbital plane at some (arbitrary) instant during the inspiral.
We test the efficacy of this parameter by considering binary inspiral
configurations specified by the physical parameters of a corresponding
non-precessing-binary configuration (total mass, mass ratio, and spin
components (anti-)parallel to the orbital angular momentum), plus the effective
precession spin applied to the larger black hole. We show that for an
overwhelming majority of random precessing configurations, the precession
dynamics during the inspiral are well approximated by our equivalent
configurations. Our results suggest that in the comparable-mass regime waveform
models with only three spin parameters faithfully represent generic waveforms,
which has practical implications for the prospects of GW searches, parameter
estimation and the numerical exploration of the precessing-binary parameter
space.
The author reports how gravitational wave observations can be used to determine the Hubble constant, H0. The nearly monochromatic gravitational waves emitted by the decaying orbit of an ultracompact, two-neutron-star binary system just before the stars coalesce are very likely to be detected by the kilometre-sized interferometric gravitational wave antennas now being designed. The signal is easily identified and contains enough information to determine the absolute distance to the binary, independently of any assumptions about the masses of the stars. Ten events out to 100 Mpc may suffice to measure the Hubble constant to 3% accuracy.